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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Electrical Engineering and Computer Science Problem Set No. 6 6.630 Electromagnetics Issued: Week 7 Fall Term 2006 Due: Week 8 -----------------------------------------------------------------------------Reading assignment: Section 2.1, 2.2; J. A. Kong, “Electromagnetic Wave Theory”. Problem P6.1 A break in a high-voltage DC power line occurs at z = 0 at time t = 0 , as shown in Fig.1. The line was carrying a DC voltage Vo and DC current Io before the break occurred. Assume that the tree is non-conducting. Power line Power line Tree Wind Fig. 1 (a) Sketch I and V on the line at some time t after the break has occurred, but before any reﬂections from the source and load ends. The characteristic impedance of the line is Z0 . (b) Consider a 600 kV line, carrying a power of 103 megawatts, with a characteristic impedance of 500 Ω (two-wire line). What is the peak voltage on the line after the break occurs? Problem P6.2 A very long transmission line with characteristic impedance Z0 and wave velocity v = c has a shunt resistor of unknown vlue RL at an unknown location z = . A measurement of the voltage at the input, V0 (t) , with a unit step generator applied to the line, yields the result shown in Fig. 2. V +’ V+ V_ Z o + Zo ,v u(t) − V (t) z = z=0 ∞ RL z V (t) 10 -8 sec t Fig. 2 (a) What is ? (b) What is RL ? (c) Sketch the voltage and current distribution on the line at the time t = 1.5/v .